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Constant angle surfaces in 2 ×. (English) Zbl 1173.53012
Let H 2 × be the Riemannian product of a two-dimensional real hyperbolic plane with constant sectional curvature -1 and a Euclidean line. The authors classify all surfaces in H 2 × for which the angle between the normal spaces of the surface and the Euclidean line in the product is constant.

MSC:
53B25Local submanifolds
References:
[1]P. Cermelli and A.J. Di Scala. Constant-angle surfaces in liquid crystals. Philosophical Magazine, 87(12) (2007), 1871–1888. · doi:10.1080/14786430601110364
[2]F. Dillen, J. Fastenakels, J. Van der Veken and L. Vrancken. Constant Angle Surfaces in S 2 × . Monaths. Math., 152(2) (2007), 89–96. · Zbl 1140.53006 · doi:10.1007/s00605-007-0461-9
[3]F. Dillen and M.I. Munteanu. Surfaces in 2 × . Pure and Applied Differential Geometry, PADGE 2007, Berichte aus der Mathematik (Shaker Verlag) Eds. Franki Dillen, Ignace Van de Woestyne, 185–193.
[4]J. Fastenakels, M.I. Munteanu and J. Van der Veken. Constant angle surfaces in the Heisenberg group, preprint.
[5]M.I. Munteanu and A.I. Nistor. A new approach on constant angle surface in E 3, to appear in Turkish J. Math., (2009).
[6]P. Petersen. Riemannian Geometry. Graduate Texts in Mathematics, Springer Verlag, (1997).
[7]J.G. Ratcliffe. Foundations of Hyperbolic Manifolds. 2-nd Edition, Graduate Texts in Mathematics, Springer (2006).